It's not likely. Alwaleed, who is worth about $18.9 billion, technically doesn't have a government position. And the Shura Council, an advisory board to the national government, rejected even studying the idea last month, The Washington Post reports. Separation of the sexes is strictly enforced in most public spaces.

But there is some popular support for the idea -- an Arabic hashtag translated as "the time has come for women's driving" trended after Alwaleed's tweet.